Factorization and Reflexivity on Fock spaces

Details Factorization and Reflexivity on Fock spaces Factorization and Reflexivity on Fock spaces

1994-04-14

arxiv.org/abs/math/9404209v1

Mathematics

Functional Analysis

Scientific paper

The framework of the paper is that of the full Fock space ${\Cal F}^2({\Cal H}_n)$ and the Banach algebra $F^\infty$ which can be viewed as non-commutative analogues of the Hardy spaces $H^2$ and $H^\infty$ respectively. An inner-outer factorization for any element in ${\Cal F}^2({\Cal H}_n)$ as well as characterization of invertible elements in $F^\infty$ are obtained. We also give a complete characterization of invariant subspaces for the left creation operators $S_1,\cdots, S_n$ of ${\Cal F}^2({\Cal H}_n)$. This enables us to show that every weakly (strongly) closed unital subalgebra of $\{\varphi(S_1,\cdots,S_n):\varphi\in F^\infty\}$ is reflexive, extending in this way the classical result of Sarason [S]. Some properties of inner and outer functions and many examples are also considered.

Affiliated with

Also associated with

No associations

Rating

Factorization and Reflexivity on Fock spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Factorization and Reflexivity on Fock spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Factorization and Reflexivity on Fock spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-246830